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Important questions on Criteria For Triangle Congruence

In the figure
Write the measure of all angles of triangle .

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Consider the following question.

Given that.

Find the value of


We know that,

In 


Therefore,


In


Hence, this is the required answer.

In figure, it is given that and . Prove that .

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In ADC and CDA

AB=CD(Given)

AD=BC(Given)

CA=CA(common)

Hence

Prove that 
 

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In and  
It is given that 
 
and  

is common 
Here , (SSS Axiom) 
Here 
(c.p.c.t) 
Therefore , it is proved 

The four triangle formed by joining the midpoints of the sides of a triangle respectively are

A

similar, not necessarily congruent.

B

congruent.

C

equilateral.

D

isosceles.

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and are mid-points of sides and .

In and

                [ Mid-point theorem ]

                [ Mid-point theorem ]

                [ Mid-point theorem ]

               [ By congruence theorem ]   --- ( 1 )

In and

                 [ is the mid-point ]

                [ Mid-point theorem ]

                [ Mid-point theorem ]

             [ By congruence rule ]     ---- ( 2 )

In and

               [ Common side ]

              [ Mid-point theorem ]

                [ Mid-point theorem ]

              [ By congruence rule ]       ----- ( 3 )

From ( 1 ), ( 2 ) and ( 3 ) we get

 

  The four triangle formed by joining the midpoints of the sides of a triangle respectively are congruent to each other.

In the following, pairs of triangles of FIg. the lengths of the sides are indicated along the sides. By applying SSS congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.

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In triangle and ,
Given,
...SSS criterion

In and in Then

A

True

B

False

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In triangle and
AB=PR=
AC=PQ=
BC=RQ=
  ..........SSS congruency

By which congruency criterion, the two triangles in Fig. are congruent?

A

B

C

D

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In triangle and ,
          ...Common
          ...Given
          ...Given
          ... criterion 
AS, all three sides are same so, it is congruent by test.
So, option is correct.

In the given figure, is an isosceles triangle in which . Also, is a point such that . then " bisects and ." is ?

A

True

B

False

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Given :
is an isosceles triangle.
 

To prove :
bisects and

Proof :
Consider and
                      [ Given ]
                     [ Given ]
                     [ Common side ]
                         [ By congruence property ]
                      [ C.P.C.T ]
                      [ C.P.CT. ]
Hence, we have proved that bisects and


In the given figure, Then is

A

equilateral

B

right angled

C

scalene

D

isosceles

View Answer

In s   and
          (Given)

          (Common)
          (SSS)
          (cpct)

          (Sides opp. equal angles are equal)
is isosceles.

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